This article is cited in 7 scientific papers (total in 7 papers)
Embedding theorems for profinite groups
V. N. Remeslennikov
Suppose that the profinite group $G$ is an extension of $A$ by $H$. In this paper the profinite subgroups of the topological group of continuous maps from $H$ to $A$ are investigated. The results obtained are used to prove topological analogues for profinite groups of the Frobenius and Magnus embedding theorems. Moreover, a sufficient condition is formulated for a pro-$p$-group that is an extension of an abelian group by a finitely presented group to be finitely presented, in the language of complete tensor products of abelian pro-$p$-groups; and this condition is used to prove that a finitely generated metabelian pro-$p$-group is a subgroup of a finitely presented metabelian pro-$p$-group.
Bibliography: 14 titles.
PDF file (1980 kB)
Mathematics of the USSR-Izvestiya, 1980, 14:2, 367–382
MSC: Primary 20E18, 22A99; Secondary 20F05
V. N. Remeslennikov, “Embedding theorems for profinite groups”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 399–417; Math. USSR-Izv., 14:2 (1980), 367–382
Citation in format AMSBIB
\paper Embedding theorems for profinite groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Jeremy D. King, “Homological finiteness conditions for pro-pgroups”, Communications in Algebra, 27:10 (1999), 4969
S. G. Melesheva, “Equations and algebraic geometry over profinite groups”, Algebra and Logic, 49:5 (2010), 444–455
S. G. Afanas'eva, N. S. Romanovskii, “Rigid metabelian pro-$p$-groups”, Algebra and Logic, 53:2 (2014), 102–113
R. Grigorchuk, R. Kravchenko, “On the lattice of subgroups of the lamplighter group”, Int. J. Algebra Comput, 2014, 1
Ch. K. Gupta, N. S. Romanovskii, “$\mathbb Q$-completions of free solvable groups”, Algebra and Logic, 54:2 (2015), 127–139
N. S. Romanovskii, “Algebraic sets in a finitely generated rigid $2$-step solvable pro-$p$-group”, Algebra and Logic, 54:6 (2016), 478–488
S. G. Afanaseva, E. I. Timoshenko, “Partially commutative metabelian pro-$p$-groups”, Siberian Math. J., 60:4 (2019), 559–564
|Number of views:|